I'm afraid I have no ideas. It might be your input signal – try plugging a guitar in directly if you do not already do so.
Do you get the clicks on both outputs ? Does it make a difference if you plug an unconnected lead into the input(s) ?
Also not clear why MIDI is different.
You could certainly send it in for us to look at (firstname.lastname@example.org), but I fear we may find nothing, meaning it may be something mysterious in your setup.